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Showing content from https://www.geeksforgeeks.org/prefix-sum-array-implementation-applications-competitive-programming/ below:

Prefix Sum Array - Implementation

Last Updated : 13 Jul, 2025

Try it on GfG Practice

Given an array arr[], Find the prefix sum of the array. A prefix sum array is another array prefixSum[] of the same size, such that prefixSum[i] is arr[0] + arr[1] + arr[2] . . . arr[i].

Examples:

Input: arr[] = [10, 20, 10, 5, 15]
Output: [10, 30, 40, 45, 60]
Explanation: For each index i, add all the elements from 0 to i:
prefixSum[0] = 10,
prefixSum[1] = 10 + 20 = 30,
prefixSum[2] = 10 + 20 + 10 = 40 and so on.

Input: arr[] = [30, 10, 10, 5, 50]
Output: [30, 40, 50, 55, 105]
Explanation: For each index i, add all the elements from 0 to i:
prefixSum[0] = 30,
prefixSum[1] = 30 + 10 = 40,
prefixSum[2] = 30 + 10+ 10 = 50 and so on.

Prefix Sum Implementation

The idea is to create an array prefixSum[] of size n, and for each index i in range 1 to n - 1, set prefixSum[i] = prefixSum[i - 1] + arr[i].

To solve the problem follow the given steps:

Declare a new array prefixSum[] of the same size as the input array
Run a for loop to traverse the input array
For each index add the value of the current element and the previous value of the prefix sum array

Below is the implementation of the above approach:

C++


 #include <iostream>
#include <vector>
using namespace std;

// function to find the prefix sum array
vector<int> prefSum(vector<int> &arr) {
    int n = arr.size();
    
    // to store the prefix sum
    vector<int> prefixSum(n);

    // initialize the first element
    prefixSum[0] = arr[0];

    // Adding present element with previous element
    for (int i = 1; i < n; i++)
        prefixSum[i] = prefixSum[i - 1] + arr[i];
    
    return prefixSum;
}

int main() {
    vector<int> arr = {10, 20, 10, 5, 15};
    vector<int> prefixSum = prefSum(arr);
    for(auto i: prefixSum) {
        cout << i << " " ;
    }
    return 0;
}

Java


 import java.util.ArrayList;

public class GfG {

    // function to find the prefix sum array
    public static ArrayList<Integer> prefSum(int[] arr) {
        int n = arr.length;

        // to store the prefix sum
        ArrayList<Integer> prefixSum = new ArrayList<>();

        // initialize the first element
        prefixSum.add(arr[0]);

        // Adding present element with previous element
        for (int i = 1; i < n; i++)
            prefixSum.add(prefixSum.get(i - 1) + arr[i]);

        return prefixSum;
    }

    public static void main(String[] args) {
        int[] arr = {10, 20, 10, 5, 15};
        ArrayList<Integer> prefixSum = prefSum(arr);
        for (int i : prefixSum) {
            System.out.print(i + " ");
        }
    }
}

Python


 # function to find the prefix sum array
def prefSum(arr):
    n = len(arr)
    
    # to store the prefix sum
    prefixSum = [0] * n

    # initialize the first element
    prefixSum[0] = arr[0]

    # Adding present element with previous element
    for i in range(1, n):
        prefixSum[i] = prefixSum[i - 1] + arr[i]
    
    return prefixSum

if __name__ == "__main__":
    arr = [10, 20, 10, 5, 15]
    prefixSum = prefSum(arr)
    for i in prefixSum:
        print(i, end=" ")


 using System;
using System.Collections.Generic;

class GfG {
   
    // function to find the prefix sum array
    static List<int> prefSum(int[] arr) {
        int n = arr.Length;
        
        // to store the prefix sum
        List<int> prefixSum = new List<int>(new int[n]);

        // initialize the first element
        prefixSum[0] = arr[0];

        // Adding present element with previous element
        for (int i = 1; i < n; i++)
            prefixSum[i] = prefixSum[i - 1] + arr[i];
        
        return prefixSum;
    }

    static void Main() {
        int[] arr = {10, 20, 10, 5, 15};
        List<int> prefixSum = prefSum(arr);
        foreach (int i in prefixSum) {
            Console.Write(i + " ");
        }
    }
}

JavaScript


 // function to find the prefix sum array
function prefSum(arr) {
    let n = arr.length;
    
    // to store the prefix sum
    let prefixSum = new Array(n);

    // initialize the first element
    prefixSum[0] = arr[0];

    // Adding present element with previous element
    for (let i = 1; i < n; i++)
        prefixSum[i] = prefixSum[i - 1] + arr[i];
    
    return prefixSum;
}

// Driver Code
let arr = [10, 20, 10, 5, 15];
let prefixSum = prefSum(arr);
for (let i of prefixSum) {
    process.stdout.write(i + " ");
}

Time Complexity: O(n)
Auxiliary Space: O(n)

Please refer Top Problems on Prefix Sum Technique for Interviews for more prefix sum problems.

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